The generation of replacement tissue in cell culture, commonly known as “tissue engineering”, the provision of surrogate cells for cell-based transplantation therapies, and the identification of new drugs using cell based high-throughput methods all represent important examples of innovative biotechnology-based applications. Stem cells in particular represent an important source for implementing such biotechnological applications because stem cells, in contrast to primary cells, can readily serve as a potentially unlimited source for obtaining differentiated, specific cell types. However, culturing stem cells, especially human embryonic stem cells, using controlled experimental conditions is not practicable according to the state of the art. Known culturing conditions are typically characterized by a lack of scalability of the cultivating process, the dependency on a co-culture system, and an inability to suitably control the experimental parameters. Until now, a scalable suspension culture of embryonic stem cells was demonstrated only for already differentiated cells known as “embryoid bodies”. Specifically, a suspension culture of embryonic stem cells in the form of embryoid bodies was established using rotating-wall bioreactors (Gerecht Nir et al., Biotechnol Bioeng. 2004, 86(5): 493-502) and known agitation systems (Zandstra et al., Tissue Eng. 2003, 9: 767-778; Dang et al., Stem Cells 2004, 22(3):2 75-82; and Wartenberg et al. Lab Invest. 1998 October; 78(10): 1301-14). Techniques utilizing a rotating-wall bioreactor are suitable for producing an organo-type-like culture via the differentiation of stem cells in order to form tissue-like aggregates; however, such techniques exhibit the disadvantage of lacking scalability to produce a larger volume of cells. Moreover, all of these known cultivation methods are characterized by significant limitations when attempting to produce differentiating and differentiated stem cells. The cultivation of undifferentiated, pluripotent cells using these known culture strategies has simply not yet been realized. Generally, the cultivation of undifferentiated primate stem cells has proven to be very complex and furthermore, particularly sensitive to external influences.